Relations between matrix sets generated from linear matrix expressions and their applications

Analytical aspects of the interval unilateral quadratic matrix equations and their united solution sets

This paper introduces the emph{interval unilateral quadratic matrix equation}, $IUQe$ and attempts to find various analytical results on its AE-solution sets in which $A,B$ and $CCC$ are known real interval matrices, while $X$ is an unknown matrix. These results are derived from a generalization of some results of Shary. We also give sufficient conditions for non-emptiness of some quasi-solutio...

2 Linear Matrix Inequality Representation of Sets

This article concerns the question: which subsets of R can be represented with Linear Matrix Inequalities, LMIs? This gives some perspective on the scope and limitations of one of the most powerful techniques commonly used in control theory. Also before having much hope of representing engineering problems as LMIs by automatic methods one needs a good idea of which problems can and cannot be re...

2 Linear Matrix Inequality Representation of Sets

Matrix Representations of Octonions and Their Applications

As is well-known, the real quaternion division algebra H is algebraically isomorphic to a 4-by-4 real matrix algebra. But the real division octonion algebra O can not be algebraically isomorphic to any matrix algebras over the real number field R, because O is a non-associative algebra over R. However since O is an extension of H by the Cayley-Dickson process and is also finite-dimensional, som...

Generalized Matrix Algebras and Their Applications

The relations between the radicals of path algebras and connectivity of directed graphs are given. The relations between radicals of generalized matrix rings and Γrings are given. All the coquasitriangular structures of group algebra kG are found when G is a finitely generated abelian group. 2000 Mathematics subject Classification: 16w30, 05Cxx.